FIG. 1 highlights the main components of a SU-MIMO transmission model of digital data. Said digital data may be encoded by using Orthogonal Frequency-Division Multiplexing (OFDM) method.
The illustrated SU-MIMO transmission model is more particularly adapted to the transmission of digital data, encoded with OFDM method, from an AP, as a transmitter 200, to a user station, as a receiver 230.
Let define the following notations used notably onto FIG. 1:                NTX is the number of transmit antennas 201, 202 of the transmitter 200;        NSS is the number of spatial streams; and        NRX is the number of receive antennas 231, 232 of the receiver 230.        
The number of spatial streams is defined as the number of data streams which are simultaneously broadcasted via the transmit antennas 201, 202. Obviously, it is mandatory that NSS≤NTX.
Let call Si(m,k) a modulated symbol, for instance a QAM (Quadrature Amplitude Modulation) symbol, sent on a kth subcarrier of a mth OFDM symbol on the ith spatial stream.
Let further define:                S(m, k)=[S1(m, k) . . . SNSS(m, k)]T, the NSS dimension multi-stream modulated symbol to be transmitted and        T(m, k)=[T1(m, k) . . . TNTX(m, k)]T, the NTX dimension multi-antenna transmit signal,where exponent T characterizes the transpose operator.        
Let have T(m, k)=Q(k)S(m, k), where Q(k) is a matrix used to convert the NSS symbols to be transmitted into NTX complex signals.
This conversion is done linearly by multiplying vectors S (m, k) of length NSS by a Q(k) matrix of dimensions NTX×NSS. Each vector of length NSS is intended to be transmitted during one OFDM symbol (In Wi-Fi, the symbol duration is often equal to 4 is, but not always) and over a given subcarrier k. The matrix Q(k), which can be called spatial mapping matrix, may vary from one subcarrier to the other, but not from one OFDM symbol to the other, during a whole packet transmission.
The spatial mapping matrix Q(k) is thus used for SU-MIMO beamforming. This technique is implemented by the transmitter 200 with multiple antennas 201, 202 to steer signals using knowledge of the physical channel between the AP and the user station in order to improve throughput or the covering range. In such a case, the transmitter 200 may be called a beamformer and the matrix Q(k) is merely called a steering matrix. It can be determined from a beamforming feedback matrix V(k) that is sent back to the beamformer 200 by the receiver 230 which may then be called beamformee, according to standard beamforming calibration processes, also called sounding processes (an example of which is detailed hereafter).
Before being emitted the NTX dimension multi-antenna transmit signal T(m, k), and more particularly each component Ti(m, k) of said signal, with i={1, . . . , NTX}, is transformed in a conventional way according to Inverse Fast Fourier Transform (or IFFT) for converting each component of said signal from its original frequency domain to a representation in the time domain.
Now, let define R(m, k)=[R1(m, k) . . . RNRX(m, k)], the signal received on the NRX antennas 231, 232 of the receiver 230.
More particularly, in a conventional way, said received signal R(m, k), and more particularly each component Ri(m, k) of said received signal, with i={1, . . . , NRX}, is obtained by transforming the radio-frequency signal received by each ith receive antenna according to Fast Fourier Transform (or FFT) for converting each component of said signal from the time domain to its original frequency domain.
Assuming an ISI (InterSymbol Interference) free transmission, and assuming that all offsets have been perfectly compensated, the frequency domain model is given by the following equation:R(m,k)=Hϕ(k)T(m,k)+WGN(m,k)R(m,k)=H(k)S(m,k)+WGN(m,k)where WGN˜N(0,σ−2) is a White Gaussian Noise, further with the assumption that all the received paths are affected by the same noise level, and where Hϕ(k) is a NRX×NTX matrix characterizing the physical channel between the antennas 201, 202 of the transmitter 200 and the ones 231, 232 of the receiver 230. H(k) is a NRX×NSS matrix characterizing the effective channel between the transmitted symbol S(m, k) and the received signal R(m, k), with: H(k)=Hϕ(k)Q(k).
In the SU-MIMO beamforming presented here above, all space-time streams of the signal to be transmitted are intended for reception at a single station 230. With DL-MU-MIMO beamforming, disjoint subsets of the space-time streams are intended for reception at different user stations.
From U.S. Pat. No. 9,319,122 B1, it is known a wireless network device, such as an AP, of a WLAN which transmits simultaneously independent data streams to at least two user stations according to a multi-user (MU) mode via an antenna array. In order to reduce, or even in order to cancel out, interference at a receiving station due to simultaneous transmissions from several antennas of the AP to one or more user stations, the AP develops respective transmit beamsteering vectors for downlink transmissions towards the user stations.
FIG. 2 highlights the main components of a DL-MU-MIMO-OFDM transmission model. The applicant's admitted prior art as discussed below in connection with FIG. 2 may be considered as an adaptation of the disclosure of document U.S. Pat. No. 9,319,122 B1 to the transmission of digital data encoded with OFDM method. Hereafter, for sake of simplicity, subcarrier index k has been omitted in comparison with the here above equations.
The transmitter (or beamformer) 200 should calculate a DL-MU-MIMO steering or pre-coding matrix Q in order to cancel out crosstalk between participating user stations 230, 240. Said DL-MU-MIMO steering matrix Q can be determined from the beamforming feedback matrices V(d) of the participating user stations 230, 240.
Let add some additional notations:                K, the number of user stations 230, 240 participating to the considered MU-MIMO transmitted frame, with K≤4 according to the standard specifications;        NSStot, the total number of spatial streams comprised in the MU-MIMO frame to be transmitted, with NSStot being constrained by NSStot≤NTX;        NSS(d), the number of spatial streams intended for the dth user station, constrained by NSS(d)<NSStot since Σd NSS(d)=NSStot; and        NRX(d), the number of receive antennas (231, 232 or 241, 242) of the dth user station (230 or 240, respectively), with NRX(d)≥NSS(d) since each stream is intended to be received by one receive antenna.        
Let further call S(d)(m)=[S1d)(m) . . . SNSS(d)(d)(m)]T the NSS(d)-dimension QAM-symbol to be transmitted to the dth user.
Then, let R(d)(m)=[R1(d)(m) . . . RNRX(d)(d)(m)]T, the NRX(d)-dimension signal received by the dth user station, verifies:R(d)(m)=H(d)[S(1)(m) . . . S(K)(m)]T+WGN(d)(m)R(d)(m)=Hϕ(d)Q[S(1)(m) . . . S(K)(m)]T+WGN(d)(m)
By splitting Q between the user stations 230, 240 as Q=[Q(1) . . . Q(K)], this equation can be decomposed into two parts:
            R              (        d        )              ⁡          (      m      )        =                    H        ϕ                  (          d          )                    ⁢              Q                  (          d          )                    ⁢                        S                      (            d            )                          ⁡                  (          m          )                      +                  ∑                              u            =            1                    ,                      u            ≠            d                          K            ⁢                          ⁢                        H          ϕ                      (            d            )                          ⁢                  Q                      (            u            )                          ⁢                              S                          (              u              )                                ⁡                      (            m            )                                +                  WGN                  (          d          )                    ⁡              (        m        )            
The first part of the equation comprises the signal of interest, whereas the second part characterizes the interference of the signal(s) transmitted to the other user station(s) on the signal received by the dth user station. As mentioned earlier, the transmitter 200 shall define the matrix Q in order to minimize, or even cancel out, the interference part for each of the K receivers 230, 240 or in order to optimize the SINR (signal-to-interference-plus-noise ratio) received by each user station.
More generally, the problem of all existing algorithms, like the one disclosed into document U.S. Pat. No. 9,319,122 B1, is that they assume that the number of receive antennas (231, 232 or 241, 242) of each user station (230 or 240, respectively) is equal to the number of spatial streams intended for this user station, e.g. NRX(d)=NSS(d). Consequently, they assume that Σd NRX(d)≤NTX.
In this context, i.e. in communication systems of the type briefly described above and notably of the type referred to as (DL-)MU-MIMO, it is an object of the invention to provide a method for obtaining a steering matrix Q to be applied for (DL-)MU-MIMO transmission that supports extended configurations of a (DL-)MU-MIMO communication system.
Another object of the invention is to provide a method for obtaining a steering matrix Q to be applied for (DL-)MU-MIMO transmission that improves significantly the quality of a (DL-)MU-MIMO transmission when the number of antennas of the receivers is larger than the number of streams intended for these receivers, that is when Σd NRX(d)≥NTX.
A further object of the invention is to provide a method for obtaining a steering matrix to be applied for (DL-)MU-MIMO transmission that offers much better performance than existing algorithms when Σd NRX(d)>NTX.